According to Green's Theorem, the Line Integral $\int _ { C } x ^ { 2 } d x + y ^ { 2 } d y$

Multiple Choice

According to Green's Theorem, the line integral $\int _ { C } x ^ { 2 } d x + y ^ { 2 } d y$ over a positively oriented, piecewise-smooth, simple closed curve C is equal to the double integral $\iint _ { D } f ( x , y ) d A$ over the region D bounded by C. Find the function $f ( x , y )$ .

A) $2 x - y$
B) $x - 2 y$
C) $2 x - 2 y$
D) $0$
E) $1$
F) $2 x + y$
G) $x + 2 y$
H) $2 x + 2 y$